In the prior art of the automatic telephone answerer, to which the invention is directed, there have been two kinds of the tape. One is the out-going message tape (hereinafter called "T-1") and another is the incoming message tape (hereinafter called "T-2"). The above two tapes are driven sequentially or simultaneously and performs the operations of sending an announcement and of taking messages. For instance, in the Japanese Pat. No. 424,747 (Application Ser. No. 36-8531), T-1 is driven at first upon receipt of a telephone call, and then T-2 is driven after T-1 stops. In the simple model of the automatic telephone answerer, for instance, the Japanese Pat. No. 491,669 (Application Ser. No. 39-7915), T-1 and T-2 are driven simultaneously upon receipt of a telephone call and the operation time of T-2 is controlled by one cycle of T-1. In the latter patent, the out-going message is pre-recorded on the first half of T-1, for instance, for 20 seconds, and a beep-tone is generated by the conventional method. Then, it can take the incoming message on T-2. However, during the above 20 seconds, T-1 and T-2 are driven simultaneously. So, there should be a 20-second blank between the previous message and the next message every time the user plays back the T-2, but the above blank of tape is regarded as an unavoidable waste in the said driving system. Among many automatic telephone answerers, there is one kind of the device as the Japanese Pat. No. 532,850 (Application Ser. No. 42-79425), which records not only the incoming message but also the out-going message on T-2 in every operation. The above tape driving system is called "simultaneous driving method" in the United States of America. For instance, the automatic telephone answerer with the trade name "Tele-Tender" on the United States market adopts the above method, but in ordinary cases, it is intricate and troublesome for general users to hear the out-going message every time before listening to every incoming message which has been recorded on T-2. It can be understood that the above 20 seconds is anyway a waste of time for users, but the above disadvantage has been regarded as an inevitable demerit in these prior arts.